SOLUTION: PROBLEM 47--PAGE 170 RE: WORD PROBLEM ON TRANSPORTATION: * ACCORDING TO DATA FROM THE NATIONAL HIGHWAY TRAFIC ADM. THE FATAL ACCIDENT RATE PER A THOUSAND LICENCED DRIVERS EVERY

Question 78135This question is from textbook MATHEMATICS: APPLICATION
: PROBLEM 47--PAGE 170
RE: WORD PROBLEM ON TRANSPORTATION:
* ACCORDING TO DATA FROM THE NATIONAL HIGHWAY TRAFIC ADM. THE FATAL ACCIDENT RATE PER A THOUSAND LICENCED DRIVERS EVERY HUNDRED MILLION MILES, CAN BE APPROXIMATED BY THE FUNCTION:::
f(X) = .0031X*2 - .291X + 7.1, where X is the age of the driver ( 16 < X < 88)
Question: AT WHAT AGE IS THE ACCIDENT RATE THE LOWEST?
NOTE: SORRY BUT,DUE TO THAT I COUN'T WRITE THE EXPRESION CORRECTLY FOR THE SYMBOLS, THE ASTERISC(*) AFTER THE X FOLLOWED BY A 2 IS AN EXPONENT 2.(EX=.0031X*2). ALSO THE SYMBOL < SHOULD BE: THE LESS THAN BACKWARD ARROW WITH A LINE UNDER THE BACKWARD ARROW LESS THAN EQUALTO IN BOTH ARROW SYMBOLS.
( I HOPE THIS HELPS WITH THE CLARIFICATION)
THANKS, A.R.

This question is from textbook MATHEMATICS: APPLICATION

Answer by stanbon(48507) (Show Source):
You can put this solution on YOUR website!
(X) = .0031X*2 - .291X + 7.1, where X is the age of the driver ( 16 < X < 88)
Question: AT WHAT AGE IS THE ACCIDENT RATE THE LOWEST?
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You have a quadratic function with coefficients a,b and c.
The mimimum occurs at x=-b/2a
x = -(-0.291)/(2*0.0031)
x = 46.935 yrs. of age
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Cheers,
Stan H.